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In this work we present an optical lattice setup to realize a full DiracHamiltonian in 2+1 dimensions. We show how all possible external potentialscoupled to the Dirac field can arise from perturbations of the existingcouplings of the honeycomb lattice model, without the need of additional laserfields. This greatly simplifies the proposed implementations, requiring onlyspatial modulations of the intensity of the laser beams. We finally suggestseveral experiments to observe the properties of the Dirac field in the setup.

Simulating Dirac fermions with Abelian and non-Abelian gauge fields in optical lattices